1234+86x*24x=345*54x+56x

Solution for 1234+86x*24x=345*54x+56x equation:

Simplifying
1234 + 86x * 24x = 345 * 54x + 56x

Reorder the terms for easier multiplication:
1234 + 86 * 24x * x = 345 * 54x + 56x

Multiply 86 * 24
1234 + 2064x * x = 345 * 54x + 56x

Multiply x * x
1234 + 2064x2 = 345 * 54x + 56x

Multiply 345 * 54
1234 + 2064x2 = 18630x + 56x

Combine like terms: 18630x + 56x = 18686x
1234 + 2064x2 = 18686x

Solving
1234 + 2064x2 = 18686x

Solving for variable 'x'.

Reorder the terms:
1234 + -18686x + 2064x2 = 18686x + -18686x

Combine like terms: 18686x + -18686x = 0
1234 + -18686x + 2064x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(617 + -9343x + 1032x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(617 + -9343x + 1032x2)' equal to zero and attempt to solve:

Simplifying
617 + -9343x + 1032x2 = 0

Solving
617 + -9343x + 1032x2 = 0

Begin completing the square.  Divide all terms by
1032 the coefficient of the squared term: 

Divide each side by '1032'.
0.5978682171 + -9.053294574x + x2 = 0

Move the constant term to the right:

Add '-0.5978682171' to each side of the equation.
0.5978682171 + -9.053294574x + -0.5978682171 + x2 = 0 + -0.5978682171

Reorder the terms:
0.5978682171 + -0.5978682171 + -9.053294574x + x2 = 0 + -0.5978682171

Combine like terms: 0.5978682171 + -0.5978682171 = 0.0000000000
0.0000000000 + -9.053294574x + x2 = 0 + -0.5978682171
-9.053294574x + x2 = 0 + -0.5978682171

Combine like terms: 0 + -0.5978682171 = -0.5978682171
-9.053294574x + x2 = -0.5978682171

The x term is -9.053294574x.  Take half its coefficient (-4.526647287).
Square it (20.49053566) and add it to both sides.

Add '20.49053566' to each side of the equation.
-9.053294574x + 20.49053566 + x2 = -0.5978682171 + 20.49053566

Reorder the terms:
20.49053566 + -9.053294574x + x2 = -0.5978682171 + 20.49053566

Combine like terms: -0.5978682171 + 20.49053566 = 19.8926674429
20.49053566 + -9.053294574x + x2 = 19.8926674429

Factor a perfect square on the left side:
(x + -4.526647287)(x + -4.526647287) = 19.8926674429

Calculate the square root of the right side: 4.460119667

Break this problem into two subproblems by setting 
(x + -4.526647287) equal to 4.460119667 and -4.460119667.

Subproblem 1
x + -4.526647287 = 4.460119667

Simplifying
x + -4.526647287 = 4.460119667

Reorder the terms:
-4.526647287 + x = 4.460119667

Solving
-4.526647287 + x = 4.460119667

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.526647287' to each side of the equation.
-4.526647287 + 4.526647287 + x = 4.460119667 + 4.526647287

Combine like terms: -4.526647287 + 4.526647287 = 0.000000000
0.000000000 + x = 4.460119667 + 4.526647287
x = 4.460119667 + 4.526647287

Combine like terms: 4.460119667 + 4.526647287 = 8.986766954
x = 8.986766954

Simplifying
x = 8.986766954

Subproblem 2
x + -4.526647287 = -4.460119667

Simplifying
x + -4.526647287 = -4.460119667

Reorder the terms:
-4.526647287 + x = -4.460119667

Solving
-4.526647287 + x = -4.460119667

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.526647287' to each side of the equation.
-4.526647287 + 4.526647287 + x = -4.460119667 + 4.526647287

Combine like terms: -4.526647287 + 4.526647287 = 0.000000000
0.000000000 + x = -4.460119667 + 4.526647287
x = -4.460119667 + 4.526647287

Combine like terms: -4.460119667 + 4.526647287 = 0.06652762
x = 0.06652762

Simplifying
x = 0.06652762

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.986766954, 0.06652762}
Solution
x = {8.986766954, 0.06652762}